Atomistic simulations based on the use of interatomic potentials and a finite element method based on the crystal plasticity theory are combined to investigate the deformation and fracture behaviour of polycrystalline lamellar gamma-TiAl + alpha(2)-Ti3Al material containing 10 vol % of body centred cubic beta phase precipitates. The effects of both stable beta phase precipitates, which deform by slip, and metastable beta phase precipitates, which deform by a combination of stress-induced martensitic transformation and slip, are studied. To model the cracking along the grain boundaries and the matrix-precipitate interfaces, the grain boundaries and interfaces are modelled using a cohesive zone approach. The grain boundary-interface potentials are determined by carrying out atomistic simulations of the grain boundary-interface normal separation (decohesion) and sliding. The results obtained suggest that incompatibilities in the plastic flow between the adjacent grains in the single-phase material give rise to a large build-up in tensile hydrostatic stress in the region surrounding certain three-grain junctions, which, in turn, leads to nucleation of the grain boundary cracks and ultimate failure. The stable beta phase precipitates located at the three-grain junctions in the two-phase material help accommodate the incompatibilities in plastic flow, doubling the strain to failure. The lattice expansion, which accompanies martensitic transformation in the metastable beta phase precipitates, further delays nucleation of the grain boundary-interface cracks giving rise to an additional increase in the fracture strain.